Base field \(\Q(\zeta_{21})^+\)
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 8 x^{2} - 8 x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[41,41,-w^{4} - 2 w^{3} + 4 w^{2} + 6 w - 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^{5} + 5 w^{3} - 5 w - 1]$ | $-2$ |
| 27 | $[27, 3, -2 w^{5} + 10 w^{3} - w^{2} - 10 w + 2]$ | $-9$ |
| 41 | $[41, 41, -w^{5} + 6 w^{3} - w^{2} - 7 w + 2]$ | $-3$ |
| 41 | $[41, 41, w^{4} - w^{3} - 4 w^{2} + 3 w + 1]$ | $-6$ |
| 41 | $[41, 41, -2 w^{5} + 12 w^{3} - 2 w^{2} - 17 w + 5]$ | $-6$ |
| 41 | $[41, 41, w^{5} - 5 w^{3} + 2 w^{2} + 5 w - 5]$ | $-3$ |
| 41 | $[41, 41, -w^{4} - 2 w^{3} + 4 w^{2} + 6 w - 3]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -2 w^{5} + 10 w^{3} - w^{2} - 10 w + 3]$ | $\phantom{-}6$ |
| 43 | $[43, 43, -w^{5} + w^{4} + 6 w^{3} - 5 w^{2} - 9 w + 4]$ | $\phantom{-}7$ |
| 43 | $[43, 43, -w^{4} - w^{3} + 4 w^{2} + 4 w - 3]$ | $-8$ |
| 43 | $[43, 43, -w^{4} + 3 w^{2} + 1]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 4 w - 2]$ | $\phantom{-}1$ |
| 43 | $[43, 43, -w^{5} + w^{4} + 6 w^{3} - 4 w^{2} - 8 w + 3]$ | $-8$ |
| 43 | $[43, 43, -w^{2} - w + 3]$ | $\phantom{-}10$ |
| 64 | $[64, 2, -2]$ | $-11$ |
| 83 | $[83, 83, -w^{5} + 6 w^{3} - w^{2} - 10 w + 4]$ | $-12$ |
| 83 | $[83, 83, -2 w^{5} + w^{4} + 12 w^{3} - 6 w^{2} - 17 w + 6]$ | $-9$ |
| 83 | $[83, 83, w^{5} - 6 w^{3} + 2 w^{2} + 8 w - 3]$ | $-15$ |
| 83 | $[83, 83, w^{5} - 4 w^{3} + w - 1]$ | $-9$ |
| 83 | $[83, 83, -2 w^{5} + 11 w^{3} - w^{2} - 13 w + 1]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41,41,-w^{4} - 2 w^{3} + 4 w^{2} + 6 w - 3]$ | $-1$ |